probability problem?

Question

A barrel contains only apples and oranges. There are twice as many apples as oranges. The apples are either red or yellow, and 4 times as many apples are red as are yellow. If one piece of fruit is to be drawn at random from the barrel, what is the probability that the piece drawn will be a yellow apple?

Answer 1

Start with Red/yellow apples:

for 1 yellow, there would be 4 red = 5 apples ...
but that would mean 2.5 oranges. So, multiply by 2 ...

For 2 yellow, there would be 8 red = 10 apples and 5 oranges

= 15 pieces of fruit.

P(yellow apple) = 2/15

Answer 2

This is a conditional probability question. To do this, the basic formula is:

P(A and B) = P(B) * P(A | B)

Where P(A | B) is the probability of A occurring given that B has happened.

Now, suppose A is the event of getting the yellow color and B is the event of getting an apple, we are looking for P(A and B).

Now, it's easiest to assume there are 15 pieces of fruit (All answers will be in proportion to this, so it doesn't matter how many there really are.)

That means, that there are 10 apples and 5 oranges. Of the 10 apples, 8 are red and 2 are yellow.

Now, P(B) = 10/15
P(A | B) = 2/10

So, the total probability is: 2/10 * 10/15 or 2/15

Answer 3

The probability of a yellow apple equals the probability that it is yellow given that it is an apple (1/5) times the probability it is an apple(2/3).
2/15

Answer 4

probability of picking an apple * probability of picking a yellow apple given you've picked an apple =

(2/3)*(1/5) = 2/15

Answer 5

let O be the number of oranges
Let A be the number of apples

A = 2O

let R be the number of red apples, let Y be the number of yellow apples
R = 4Y

R + Y = A

we know that A = 2O
so, R + Y = 2O

we know that R = 4Y
so, 4Y + Y = 2O
5Y = 2O
Y = 2O/5

favor outcome
--------------
total outcome

2O/5 is the number of Yellow Apples and also the number of favor outcome

The total outcome is the number of Orange + Apples
we know that are O (letter O) number of orranges, so, there are 2O number of Apples.

2O + O = 3O ==> number of total outcome

(5O/5) / (3O )

= 2O/5 * 1/3O

= 2/5 * 1/3

= 2/15

so the probability of getting a yellow apple is 2/15

Answer 6

let the number(no.) of yellow apples be x.
thus, the no. of red apples=4*x =4x
total no. of apples=x=4x=5x
no. of oranges=1/2(no. of apples) = 5x/2

total no. of fruits = 5x+(5x/2)= 15x/2

probability of drawing yellow apple= x/(15x/2) =2x/15x=2/15
ans=2/15

Answer 7

x = # of oranges
2x = # of apples
3x = total apples and oranges
.8*2x = 1.6x = number of red apples
.2*2x = .4x = number yellow apples
So P = .4x/3x = .13333333333.....